1. Field of the Invention
The present invention relates to a method of fabricating a reflecting mirror for a reflecting telescope and, more specifically, to a method of fabricating a reflecting mirror for a reflecting telescope, consisting of mirror segments arranged and stuck together so that the thermal deformation of the reflecting mirror attributable to the difference in coefficient of thermal expansion (hereinafter CTE) between the component mirror segments is reduced to a minimum.
2. Description of the Prior Art
FIG. 1 is a perspective view of a reflecting mirror formed by sticking mirror segments together. A reflecting mirror as shown in FIG. 1 (b) is formed by sticking together a plurality of hexagonal mirror segments (hereinafter referred to as "stacks") 2, such as shown in FIG. 1(a). The surface of the reflecting mirror 1 is finished by polishing in, for example, a paraboloid or a hyperboloid in an accuracy on the order of 1/100 of the observation wavelength to reflect and focus an electromagnetic wave, such as visible light and infrared rays. If the surface of the reflecting mirror 1 is finished in a perfect paraboloid, the incident electromagnetic wave emitted by a celestial body is converged on a single point (the focus). Practically, the incident electromagnetic wave is not focused in an image having a diameter virtually equal to zero due to the diffraction of light, and there is a theoretical limit in the diameter of the image, determined by the aperture D of the reflecting mirror and the wavelength .lambda. of the incident electromagnetic wave.
FWHM (full width at half maximum) in the theoretical limit image, in general, is expressed by EQU FWHM=1.02.times.(.lambda./D) rad=2.1.times.10.sup.5 .times.(.lambda./D) arcsec (1)
FWHM is the width between two values on the horizontal axis of a graph showing a light intensity distribution curve, for which light intensity is one-half the maximum light intensity as shown in FIG. 2. Accordingly, a theoretical limit in the size of the image of a star is dependent on the aperture D of the reflecting mirror 1 and the wavelength .lambda. of the incident electromagnetic wave. That is, theoretical limit is smaller and light gathering power is higher when the aperture D is larger. Accordingly, increase in the aperture of the reflecting mirror 1 enables reduction in size of the image and hence is a significant contribution to the improvement of resolution, the improvement of limit of detection and reduction in exposure time.
However, in practice, the reflecting mirror 1 is subject to thermal deformation according to temperature variation because the CTES of the stacks 2 are not zero. If all the stacks 2 are the same in thermal expansion coefficient, only the focus of the reflecting mirror 1 may be changed by the change of temperature and the image quality is not deteriorated because the shape of each stack 2 before thermal change and that of the same after thermal change are similar. However, in practice, the stacks 2 differ from each other in CTE, the reflecting mirror 1 is subject to irregular thermal deformation.
Since the number of the component stacks 2 of the reflecting mirror 1 increases with the aperture D of the reflecting mirror 1, the irregularity in thermal deformation of a larger reflecting mirror is more complex, and slight tilt of the reflecting mirror due to thermal deformation causes a significant thermal deformation of the same. Thus, if thermal deformation occurs in the reflecting mirror, incident light received from a celestial body is scattered to form a blurred image having a light intensity distribution as indicated by continuous line in FIG. 3(b) and, consequently, it is impossible to make most of the foregoing advantages of increase in the aperture of the reflecting mirror 1.
One kind of inhomogeneity in the respective CTES of the stacks 2 that cause the irregular thermal deformation of the reflecting mirror is the difference between the stacks 2 in the gradient of CTE with respect to the direction of thickness of the stacks 2, which cause a bimetal effect, and another kind is the difference between the stacks 2 in average CTE. A prior art method proposed to suppress the thermal deformation to the least extent arranges stacks as shown in FIG. 4.
In FIG. 4, .DELTA..alpha..sub.1 to .DELTA..alpha..sub.37 (.DELTA..alpha..sub.1 .gtoreq..DELTA..alpha..sub.2 .gtoreq. . . . .DELTA..alpha..sub.37) are the deviations of the respective average CTEs of stacks 2 from the average of the CTEs of all the stacks 2. The stacks 2 are classified into three groups, namely, a group of those having larger deviations (represented by segments shaded by crossing oblique lines), a group of those having middle deviations (represented by segments shaded by dots) and a group of those having smaller deviations (represented by blank segments).
This prior art method arranges the stacks 2 of different groups as shown in FIG. 4, in which stacks 2 included in the group of stacks 2 having middle deviations and stacks 2 included in the group of stacks having smaller deviations are arranged around each stack 2 included in the group of stacks having larger deviations. This arrangement relaxes the large thermal expansion of the stack 2 having a large deviation to some extent by the relatively small thermal expansions of the stacks 2 surrounding the former to limit deformation of the reflecting mirror 1 to local deformation. The deformation of the reflecting mirror formed by arranging the stacks in this arrangement by the prior art method is expected intuitively to be far smaller than that of a reflecting mirror in which the distribution of the CTEs of the stacks is localized.
FIG. 5 is a sectional view of a reflecting mirror provided with actuators for correcting thermal deformation. Temperature sensors 3 are attached to the backside of the reflecting mirror 1, a data processing unit 4 calculates correcting forces on the basis of the temperature of the reflecting mirror 1 measured by the temperature sensors 3, and an actuator controller 5 controls actuators 6 to apply appropriate correcting forces to the reflecting mirror 1 to correct the thermal deformation of the same.
If it is desired to correct the thermal deformation perfectly by the actuators 3, irregularities of small pitches must be corrected, which requires a large force for correction and hence is practically impossible. Accordingly, the deformation is expanded in a series of finite or infinite terms as a function of spatial frequency, and only the terms having large pitches of irregularity are corrected. The residual deformation of the mirror surface due to irregularities of small pitches which have not been corrected deteriorates the quality of the image.
FIG. 6 shows an arrangement of stacks entailing intuitive expectation that thermal deformation occur locally in the terms having large pitches of irregularity in correcting only the terms having large pitches of irregularity. In FIG. 6, .DELTA..alpha.hd 1 to .DELTA..alpha..sub.37 of the stacks 2 correspond respectively to those of the stacks 2 shown in FIG. 4.
Since the prior art reflecting mirror is thus fabricated, in which the arrangement of the stacks is determined intuitively. Accordingly, such an arrangement of stacks is not necessarily effective for reducing the thermal deformation to the least extent.